References

This page contains the bibliography for the AMS Notices article:  Time-frequency analysis of musical rhythm.  Many of the references are available for  downloading by clicking on the appropriate link.

[1]  J.F. Alm and J.S. Walker. Time-frequency analysis of musical instruments.  SIAM Review, Vol. 44 (2002), 457-476.   (Download)

[2]  J. S. Bach, (arranged and adapted by M. Scott), Jesu, Joy of Man's Desiring.  A free version of the part of the score used for the clip analyzed can be obtained by clicking here.

[3]  Balazs, P. et al. Double preconditioning for Gabor frames.  IEEE Trans. on Signal Processing,  Vol. 54 (2006), 4597-4610.   (Download)

[4]  L. Bernstein. The World of Jazz, pp. 106-131, The Joy of Music, Amadeus Press, Pompton Plains, NJ, 2004.

[5]  D. Brubeck, Unsquare Dance.  The beginning of the score, containing the hand-clapping introduction, can be viewed for free by clicking here.

[6]  X. Cheng, et al., Making Pictures of Music: New Images and Videos of Musical Sound.  To go to this webpage, click here.
Examples of more analyses of rhythmic percussion can be found by clicking here.

[7]  N. Chomsky.  Syntactic Structures.  Mouton de Gruyter, New York, 2002.

[8]  C.K. Chui.  Wavelets: A Mathematical Tool for Signal Analysis.  SIAM, Philadelphia, PA, 1997.

[9]  R. Cogan.  New Images of Musical Sound.  Harvard University Press, Cambridge, MA, 1984.

[10]  I. Daubechies.  Ten Lectures on Wavelets.  SIAM, Philadelphia, PA, 1992.

[11]  I. Daubechies and S. Maes.  A nonlinear squeezing of the continuous wavelet transform based on auditory nerve models. In Wavelets in Medicine and Biology, pp. 527-546, CRC Press, Boca Raton, FL, 1996.

[12]  M. Dörfler.  Gabor Analysis for a Class of Signals called Music. Dissertation, University of Vienna, 2002.   (Download)

[13]   M. Dörfler.  Time-Frequency Analysis for Music Signals-a Mathematical Approach.  Journal of New Music Research,
Vol. 30, No.1, March 2001.   (Download)

[14]  M. Dörfler and H.G. Feichtinger. Quantitative Description of Expression in Performance of Music, Using Gabor Representations.  Proceedings of the Diderot Forum on Mathematics and Music, 1999, Vienna. 

[15]  H. Feichtinger and T. Strohmer, eds., Gabor Analysis and Algorithms.  Birkhauser, Boston, MA, 1998.

[16]  H. Feichtinger and T. Strohmer, eds.,  Advances in Gabor Analysis.  Birkhauser, Boston, MA, 2002.

[17]  D. Gabor. Theory of communication.  Journal of the Institute for Electrical Engineers, Vol. 93 (1946), 873-880.

[18]   Erroll Garner recording on YouTube.  To veiw this video, click here.

[19]   K. Gröchenig.  Foundations of Time-Frequency Analysis. Birkhauser, Boston, MA, 2001.

[20]  L. Harkleroad.  The Math Behind the Music.  Cambridge University Press, Cambridge, UK, 2006.

[21]  D. Kroodsma.  The Singing Life of Birds.  Houghton-Mifflin, NY, 2005.

[22]  F. Lerdahl and R. Jackendoff.  A Generative Theory of Tonal Music. MIT Press, Cambridge, MA, 1983.

[23]  F. Lerdahl and R. Jackendoff.  An Overview of Hierarchical Structure in Music.  In Machine Models of Music (1992), S.~Schwanauer and D.~Levitt, eds., MIT Press, Cambridge, MA, 289-312.

[24]  D. Levitin. This Is Your Brain On Music.  Dutton, New York, 2006.

[25]  G. Loy.  Musimathics: The Mathematical Foundations of Music, Vol. 2. MIT Press, Cambridge, MA, 2007.

[26]  F.B.Mache.  Music, Myth and Nature. Contemporary Music Studies, Vol. 6.  Taylor & Francis, London, 1993.

[27]  S. Mallat.  A Wavelet Tour of Signal Processing. Second Edition.  Academic Press, San Diego, CA, 1999.

[28]  S. Pinker.  How the Mind Works.  Norton, NY, 1997.

[29]  L. Prima, Sing Sing Sing.  The initial part of the score, containing the drum solo introduction, can be viewed for free by clicking here.

[30]  D. Rothenberg. Why Birds Sing: A Journey into the Mystery of Bird Song.  Basic Books, NY, 2005.

[31]  W. Sethares.  Rhythm and Transforms.  Springer, New York, NY, 2007.

[32]   L.M. Smith.  Modelling rhythm perception by continuous time-frequency analysis.  Proceedings of the 1996 International Computer Music Conference,  Hong Kong, 392-395.   (Download)

[33]  L.M. Smith. A multiresolution time-frequency analysis and interpretation of musical rhythm, thesis, University of Western Australia, 2000.   (Download)

[34]  J.S. Walker. A Primer on Wavelets and their Scientific Applications, Second Edition.   Chapman & Hall/CRC Press, Boca Raton, FL, 2008.  Material referenced from Chapters 5 and 6 is available by clicking  here (chap. 5)  or  here (chap. 6).

[35]  J.S. Walker.  Document on using Audacity and  Fawav.   (Download) 

[36]  J.S. Walker and G.W. Don.  Music:  A time-rrequency approach.  Preprint.  (Download)